HP Voyager Programs
For HP-15C

This program, STO_MAT, provides a fast way to dimension & fill a real or complex matrix. This program can Generally reduce keystroke overhead in half.

When flag 8 is clear, the real part of the value in the X stack level is placed in consecutive matrix elements.

When flag 8 is set, the program provides extra help in filling a C format complex matrix. In this case, the real & complex parts of the number in the X stack level are used to fill consecutive matrix elements. If all the matrix elements are known in advance and in rectangular format, then fewer keystrokes will be required with 8 clear:

That said, setting flag 8 is very useful if some computation with the elements is required before we store them – like converting them to rectangular form with →R.

• Operation
  • Run the program with the following inputs:
    • Z: A matrix descriptor or number 0 (a 0 indicates the A matrix should be used)
    • Y: number of rows
    • X: Number of columns
  • The matrix element coordinate will appear on the display in r.c format.
  • The previously entered element, if there was one, will be on level Y of the stack.
  • Enter the value for the matrix position and press R/S.
    • If flag 8 is set, then the real and complex parts will be placed into the matrix in consecutive positions.
  • Repeat until all the matrix elements have been entered.
  • Note the program never ends – it just wraps back to the start.

• Entry Point Label:
  • 7 STO_MAT – STO_MAT on the left and RCL_MAT on the right – just like the STO & RCL buttons.
• Internal Labels:
  • .1 Main loop target
  • .2 Complex if target
• External Labels:
  • None
• Flags:
  • 8 Option flag (complex mode)
  • 9 CF used as NOP
• Registers Used:
  • 0 Matrix indexing
  • 1 Matrix indexing
  • I Matrix descripter
• Matrices:
  • Matrix on stack level X when the program starts, or matrix A if X was zero.

This program, RCL_MAT, provides a fast way iterate over the elements of a real or complex matrix.

• Operation
  • Run the program with the following inputs:
    • X: A matrix descriptor or number 0 (a 0 indicates the RESULT matrix should be used)
  • Each element of the matrix will be displayed. Press R/S to advance.
    • The program will wrap around to the first element after the last one is displayed – this is a feature.
    • If flag 8 is set, then pairs of elements are pulled from the matrix (i.e. C format) and placed on the stack as complex numbers

• Entry Point Label:
  • 8 RCL_MAT – STO_MAT on the left and RCL_MAT on the right – just like the STO & RCL buttons.
• Internal Labels:
  • .3 Main loop target
  • .4 Complex if target
• External Labels:
  • None
• Flags:
  • 8 Option flag (complex mode)
  • 9 CF used as NOP
• Registers Used:
  • 0 Matrix indexing
  • 1 Matrix indexing
  • I Matrix descripter
• Matrices:
  • Matrix on stack level X when the program starts, or RESULT if X was zero.

This program solves the system \(AX=B\) for \(X\).

• Program start conditions
  • The \(A\) matrix is stored in A.
    • It may be an \(n\times n\) real matrix, or an \(n\times 2n\) complex matrix in C format.
    • The program determines real vs. complex from the matrix size – not the setting of flag 8.
  • The \(B\) matrix is stored in B.
  • Flag 1 is set appropriately:
    • Clear: Use more memory, but preserve contents of A.
    • Set: Use less memory, but destroy contents of A.
• Program end conditions
  • The system "solution", \(X\), will be in C. Note this might not be a valid solution if \(A\) is singular!
  • B is left unchanged!
  • The matrix descriptor for C will be in stack position Y.
  • Matrix C will be selected as the RESULT matrix.
  • Both registers 0 & 1 will contain 1 in expectation USER mode will be used to visit the elements of C.
  • If \(A\) is a real matrix:
    • Flag 0 will be clear
    • \(\mathrm{det}(A)\) is in stack position X
    • The LU factorization of \(A\) is in E when flag 1 is clear, and in A otherwise
  • If \(A\) is a complex matrix
    • Flag 0 will be set
    • \(\vert\mathrm{det}(A)\vert\) is in stack position X.
    • The LU factorization of \(\tilde{A}\) is in E when flag 1 is clear, and in A otherwise

• Entry Point Label:
  • 8 Program label
• Internal Labels:
  • None
• External Labels:
  • 9 Subroutine to compute determinant
• Flags:
  • 0 Status flag
  • 1 Option flag
• Registers:
  • None
• Matrices:
  • A
  • B
  • C Used for the solution
  • E Only when flag 1 is clear

• Program start conditions
  • The \(A\) matrix is assumed to be in A.
    • It may be an \(n\times n\) real matrix, or an \(n\times 2n\) complex matrix in C format.
    • The program determines real vs. complex from the matrix size.
  • flag 1 is set appropriately:
    • Clear: Use more memory, but preserve contents of A.
    • Set: Use less memory, but destroy contents of A.
• Program end conditions
  • The previous contents of the stack are lost
  • If flag 1 is clear
    • A is left unchanged!
    • RESULT matrix set as E
  • If flag 1 is set
    • RESULT matrix set as A
  • \(A\) is a real matrix
    • Flag 0 will be clear
    • The \(\mathrm{det}(A)\) is in stack position X.
    • The LU factorization of \(A\) is in E when flag 1 is clear, and in A otherwise
  • If \(A\) is a complex matrix
    • Flag 1 will be set
    • \(\vert\mathrm{det}(A)\vert\) is in stack position X.
    • The LU factorization of \(\tilde{A}\) is in E when flag 1 is clear, and in A otherwise

• Entry Point Label:
  • 9 Program label
• Internal Labels:
  • None
  • .9 Conditional label
• External Labels:
  • N/A
• Flags:
  • 0 exit flag
  • 1 option flag
• Registers:
  • N/A
• Matrices:
  • A
  • E Only when flag 1 is clear